Communication Steps for Parallel Query Processing
Bibliographic record
Abstract
We study the problem of computing conjunctive queries over large databases on parallel architectures without shared storage. Using the structure of such a queryqand the skew in the data, we study tradeoffs between the number of processors, the number of rounds of communication, and the per-processorload—the number of bits each processor can send or can receive in a single round—that are required to computeq. Since each processor must store its received bits, the load is at most the number of bits of storage per processor. When the data are free of skew, we obtain essentially tight upper and lower bounds for one round algorithms, and we show how the bounds degrade when there is skew in the data. In the case of skewed data, we show how to improve the algorithms when approximate degrees of the (necessarily small number of) heavy-hitter elements are available, obtaining essentially optimal algorithms for queries such as skewed simple joins and skewed triangle join queries. For queries that we identify astreelike, we also prove nearly matching upper and lower bounds for multi-round algorithms for a natural class of skew-free databases. One consequence of these latter lower bounds is that for any ε > 0, usingpprocessors to compute the connected components of a graph, or to output the path, if any, between a specified pair of vertices of a graph withmedges and per-processor load that isO(m/p1−ε) requires Ω(logp) rounds of communication. Our upper bounds are given by simple structured algorithms using MapReduce. Our one-round lower bounds are proved in a very general model, which we call theMassively Parallel Communication (MPC)model, that allows processors to communicate arbitrary bits. Our multi-round lower bounds apply in a restricted version of the MPC model in which processors in subsequent rounds after the first communication round are only allowed to send tuples.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".